At present

some methods have been presented to calculate the degree of similarity between (Fuzzy numbers

FNs) or (Generalized fuzzy numbers

GFNs) Most of them are designed for standardized fuzzy numbers

i.e.

the universe of the discourse of FNs lie in unit interval.In order to deal with the non-standardized fuzzy numbers common in practice

it is necessary to transform it into standardized fuzzy numbers

such that the degree of similarity can be calculated.However

normalization process tends to cause information loss and unreasonable results of similarity measure.This paper presents a new similarity measure between GTFNs avoiding normalization process.The new method combines the concepts of exponential distance

the perimeter and the area of GTFNs for calculating the degree of similarity.Some properties of the proposed similarity measure are also proved.And then 12 typical sets of GFNs are given to compare the proposed method with most of the existing methods.The results show that the new method is more efficient to a certain extent.Finally

a practical example is given to show that the proposed method can provide a useful way to deal with the problem of D-S evidence theory based machinery fault diagnosis.